SPACE MATHEMATICS WORKSHEET 1 Astronomical Units and light-years Some problems adapted from http://www.grc.nasa.gov Name: _____________________ Conversion Factors: 1 AU ≈ 1.496 x 108 kilometers = 1.496 x 1011 meters 1 mile = 1.61 km = 1610 meters speed of light = 3 x 108 meters/second 1 year = 31,556,926 seconds 1 mile = 5280 feet mass of the Sun = 1.98892 × 1030 kilograms Luminosity of our Sun = 3.839×1026 Watts 1) Find the earth-sun distance, in miles. Round to three significant figures. 2) For each of the following NEWLY DISCOVERED celestial bodies, below, the mean distance from the sun is given in kilometers. Fill in the data table by expressing these distances in AU's, using three significant figures for each result. Distance Distance Celestial Body (kilometers) (Astronomical Units) Planet Z 0.58 x 108 Comet Y 1.08 Star X 2.27 x 108 Moon W 7.78 x 108 x 108 3) Green Fuzzy Aliens: a) Find the length of one light year in kilometers. b) Find the length of one light-year in AU's. c) A fuzzy green alien travels for three light years to arrive on Earth. How far did it travel, as measured in kilometers? d) A fuzzy green alien travels for 1/2 light years, after it leaves Earth again. How far did it travel, as measured in AU's? e) Compared to our distance from the sun, how many times greater is the distance the alien traveled AWAY from Earth? f) If a light wave left Earth at the same moment, traveling in the same direction as the alien, where would it be relative to the alien after each traveled 1/2 light year? 4) Convert 2.05 x 105 seconds into years. The Earth rotates. The moon rotates. Have you ever wondered if the Sun rotates (i.e. does it spin on its axis?) The Sun does indeed rotate. Galileo noted this nearly 400 years ago when he observed sunspots. The apparent motion of sunspots can be used to determine the rotation speed of the Sun. As it turns out, the Sun's rotation is quite different from that of most of the planets. A rigid body such as the Earth will clearly have a single rotation rate. But since the Sun is made of gas, different parts of it rotate at different speeds. Near the Sun's equator, it completes one rotation every 27 Earth days. But near the poles, it's about 31 Earth days. This is called "differential rotation". 5. Problem: When a solar flare occurs on the Sun, it can send out a blast wave that travels through interplanetary space at a speed of 3 x 106 km/h. a. How long would it take a blast wave to get to Earth where it could be detected by a satellite in orbit? The EarthSun distance is 1.5 x 108 km , and you can use the same number for the satellite-Sun distance. Express your answer in hours. b. When such a solar flare is detected, it is interesting to study the source. Since the Sun is rotating, we must determine how far the source has turned between the emission and the detection of a solar flare. Because the Sun is a dense gas rather than a solid body, it does not have uniform rotation rate; on the average the Sun makes one complete revolution in 25.4 days. How many degrees would it rotate (on the average) during the time the blast wave traveled from the sun to the orbiting satellite? Pioneer 10 (also known as Pioneer F) is a 258-kilogram robotic space probe that completed the first interplanetary mission to Jupiter, and became the first spacecraft to achieve escape velocity from our Solar System. 5 6) Pioneer 10's radio signals left Pluto in April 1983. They traveled at the speed of light (3.00 x 10 km/s). How long did 9 the radio signals take to reach Earth, a distance of 4.58 x 10 km ? Express your answer in hours. 9 7) Pioneer 10 traveled about 4.58 x 10 km between March 3, 1972 and April 25, 1983. Use an approximation of 11 years to determine the average speed of Pioneer 10 in km/h? 8) Use your answer to Question #7 to determine the speed of Pioneer 10 in miles/hour. 9) Use the mass of the Sun and the mass of Pioneer 10 to determine the relative mass 22 10) Pioneer 10 traveled to Pluto. The mass of Pluto is 1.3 × 10 kilograms. Determine the relative mass of Pluto. 11) In November, 1973, the spacecraft came within 132,252 km of the outer atmosphere of Jupiter, with a mass of 1.8987 × 1027 kilograms. Determine the relative mass of Jupiter. Scientists Discover Star Hundreds of Times Heavier Than the Sun (07/22/2010) Astronomers from Britain have discovered the heaviest star known in the universe, over 250 times more massive than our Sun and shining 10 million times more brightly. The star, R136a1, was found in a galaxy next to our own. Other astronomers caution not to get too excited by the find because, though the British team have a strong case, R136a1 may actually be a pair of stars. 12) Assuming the British scientists are correct and the mass really does have a relative mass of 250 MSun, what is the weight of R136a1 in kilograms? 13) What is the Luminosity of R136a1? Use the information in the data table at the top of this worksheet! Include units in your answer.